What is the impact of sample size? If the study had been done with a sample of 25, and found a difference of 1.3 points, would we come to the same conclusion?
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STATISTICAL INFERENCE: Working with Distributions Problem Set 4 ___________________________________________________________________________ Don't Miss This Fabulous Offer! Increase your chances of getting into Med School O Subscribe now to Captain Caplan’s Cookbook Course and raise your MCAT score by at least 2 full points O A scientific study of 100 potential applicants showed a significant gain (P<.05)>
Microsoft Word - Problem Set 04 2012 STATISTICAL INFERENCE: Working with Distributions Problem Set 4 ___________________________________________________________________________ Don't Miss This Fabulous Offer! Increase your chances of getting into Med School O Subscribe now to Captain Caplan’s Cookbook Course and raise your MCAT score by at least 2 full points O A scientific study of 100 potential applicants showed a significant gain (P<.05) after only six weeks of the fantastic cccc program. you owe it to yourself! the graph of mcat scores based on the actual 2006 administration is shown below. as the graph shows, this distribution has a mean of 25.6, standard deviation of 6.4 intekhab hossain highlight as it turns out, the actual difference detected in the “study” was 1.3 points. a) the first question we are asking is: what is the likelihood that a difference of 1.3 points or more in mcat score, based on a simple randomly sample of 100 applicants, could arise by chance under the null hypothesis that the treatment had no effect.? the study claims this likelihood is less than 5%. how did they arrive at that figure? intekhab hossain highlight b) a second question is this. they claim that the course is guaranteed to gain 2 points. assuming that their calculations are right, what is the likelihood that a difference of 1.3 points or less could arise by chance, in a randomly selected sample of 100 applicants under the alternative hypothesis that the treatment had a true effect of 2 points? an alternative way to ask the question is , what is the likelihood that a difference of 1.3 points or more could arise by chance, in a randomly selected sample of 100 applicants under the alternative hypothesis that the treatment had a true effect of 2 points? what is the power of the test to detect a difference of 2 points? c) a third question is this. what is the impact of sample size? if the study had been done with a sample of 25, and found a difference of 1.3 points, would we come to the same conclusion? intekhab hossain highlight intekhab hossain highlight intekhab hossain highlight intekhab hossain highlight intekhab hossain highlight intekhab hossain highlight intekhab hossain sticky note read page 50-52 after="" only="" six="" weeks="" of="" the="" fantastic="" cccc="" program.="" you="" owe="" it="" to="" yourself!="" the="" graph="" of="" mcat="" scores="" based="" on="" the="" actual="" 2006="" administration="" is="" shown="" below.="" as="" the="" graph="" shows,="" this="" distribution="" has="" a="" mean="" of="" 25.6,="" standard="" deviation="" of="" 6.4="" intekhab="" hossain="" highlight="" as="" it="" turns="" out,="" the="" actual="" difference="" detected="" in="" the="" “study”="" was="" 1.3="" points.="" a)="" the="" first="" question="" we="" are="" asking="" is:="" what="" is="" the="" likelihood="" that="" a="" difference="" of="" 1.3="" points="" or="" more="" in="" mcat="" score,="" based="" on="" a="" simple="" randomly="" sample="" of="" 100="" applicants,="" could="" arise="" by="" chance="" under="" the="" null="" hypothesis="" that="" the="" treatment="" had="" no="" effect.?="" the="" study="" claims="" this="" likelihood="" is="" less="" than="" 5%.="" how="" did="" they="" arrive="" at="" that="" figure?="" intekhab="" hossain="" highlight="" b)="" a="" second="" question="" is="" this.="" they="" claim="" that="" the="" course="" is="" guaranteed="" to="" gain="" 2="" points.="" assuming="" that="" their="" calculations="" are="" right,="" what="" is="" the="" likelihood="" that="" a="" difference="" of="" 1.3="" points="" or="" less="" could="" arise="" by="" chance,="" in="" a="" randomly="" selected="" sample="" of="" 100="" applicants="" under="" the="" alternative="" hypothesis="" that="" the="" treatment="" had="" a="" true="" effect="" of="" 2="" points?="" an="" alternative="" way="" to="" ask="" the="" question="" is="" ,="" what="" is="" the="" likelihood="" that="" a="" difference="" of="" 1.3="" points="" or="" more="" could="" arise="" by="" chance,="" in="" a="" randomly="" selected="" sample="" of="" 100="" applicants="" under="" the="" alternative="" hypothesis="" that="" the="" treatment="" had="" a="" true="" effect="" of="" 2="" points?="" what="" is="" the="" power="" of="" the="" test="" to="" detect="" a="" difference="" of="" 2="" points?="" c)="" a="" third="" question="" is="" this.="" what="" is="" the="" impact="" of="" sample="" size?="" if="" the="" study="" had="" been="" done="" with="" a="" sample="" of="" 25,="" and="" found="" a="" difference="" of="" 1.3="" points,="" would="" we="" come="" to="" the="" same="" conclusion?="" intekhab="" hossain="" highlight="" intekhab="" hossain="" highlight="" intekhab="" hossain="" highlight="" intekhab="" hossain="" highlight="" intekhab="" hossain="" highlight="" intekhab="" hossain="" highlight="" intekhab="" hossain="" sticky="" note="" read="" page="">